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Adding and Subtracting Decimals

Learning text on the topic Adding and Subtracting Decimals

Adding and Subtracting Decimals

Welcome to the world of Adding and Subtracting Decimals! Today, we'll explore how to add and subtract decimal numbers using strategies based on place value. We'll ensure you understand this fundamental concept and feel confident in applying it!

Understanding Adding and Subtracting Decimals

Adding and subtracting decimals is the process of combining or taking away amounts that are represented in tenths, hundredths, or even smaller units, by ensuring that the decimal points are aligned.

Adding decimal numbers and subtracting decimal numbers might seem tricky at first, but using your knowledge of place value and careful alignment of digits, it becomes like adding and subtracting with whole numbers, using methods that you are already familiar with.

Like with whole numbers, you always align the numbers by place value, making sure the decimal place is aligned too. You can use a place value chart to help you align your numbers correctly.

27591_ToV_Adding_and_Subtracting_Decimals-01.svg

If one of the numbers you are adding or subtracting has fewer digits in the decimal places, you can annex, or add, zeros to make the digits the same length. This helps with aligning for addition and subtraction.

Adding and Subtracting Decimals – Rules

If you are wondering how to add decimals or how to subtract decimals, you can follow step-by-step rules for each operation. Below are the rules for you to learn and follow.

Operation Step Description
Adding Decimals Step 1 Line up the decimal points of the numbers vertically.
Step 2 If necessary, add zeros to make the decimal parts equal in length.
Step 3 Add the numbers as you would with whole numbers.
Step 4 Bring the decimal point straight down into your answer.
Subtracting Decimals Step 1 Line up the decimal points of the numbers vertically.
Step 2 If necessary, add zeros to the end of the decimal part to make them equal in length.
Step 3 Subtract the numbers as you would with whole numbers.
Step 4 Bring the decimal point straight down into your answer.

Let’s check-in by answering some questions about what we have learned so far!

What do you do if one decimal has fewer digits?
Why is place value important in this process?

Adding and Subtracting Decimals – Step-By-Step Examples

Let’s walk through a decimal addition example to make sure you understand the process of adding decimals. Let's solve: 3.75 + 2.6.

  • First, align the decimals, adding a zero in the hundredth place for 2.6:

27591_ToV_Adding_and_Subtracting_Decimals-02.svg

  • Then, add as you would with whole numbers, keeping the decimal point in the same place:

27591_ToV_Adding_and_Subtracting_Decimals-03_(1).svg

The answer for 3.75 + 2.6 is 6.35.

Now let’s walk through another example, this time for subtracting decimals. Let’s solve: 5.8 - 2.35.

  • First, align the decimals, adding a zero in the hundredths place for 5.8.

27591_ToV_Adding_and_Subtracting_Decimals-04.svg

  • Then, subtract as you would with whole numbers, keeping the decimal point in the same place:

27591_ToV_Adding_and_Subtracting_Decimals-05_(1).svg

Adding and Subtracting Decimals – Guided Practice

Now we will walk through an example together. Let's solve: 5.82 - 3.4.

What is the first step?
What is the next step?
What is the answer for 5.82 - 3.4?

Adding and Subtracting Decimals – Exercises

Now you are ready for some decimal addition and subtraction practice on your own! For the first problem solve 7.53 - 4.6.

What is 7.53 - 4.6?

For the next problem, solve 8.75 + 3.42.

What is 8.75 + 3.42?

Adding and Subtracting Decimals – Summary

You can use place value to add and subtract decimal numbers, by following these steps:

  • Align decimal points and ensure equal length by adding zeros.
  • Add or subtract as with whole numbers.
  • Remember the importance of place value for accurate calculation.
  • Always check your answer.

Practice these steps to build your confidence and skill in decimal addition and decimal subtraction.

Explore more about Adding and Subtracting Decimals with our interactive practice problems, engaging videos, and printable worksheets on our learning platform. Your journey in mastering decimals is just beginning! Check out videos on Adding Decimals using Place Value and Subtracting Decimals using Place Value for extra practice in this topic.

Adding and Subtracting Decimals – Frequently Asked Questions

Can I add or subtract decimals without aligning them first?
What if there are different numbers of digits after the decimal point?
Why do we add zeros in decimal subtraction?
How do I know where to place the decimal point in the answer?
Can I use these methods for decimals with more than two places?
Is it necessary to always write zeros after the decimal if there is no value?
Are there any tools to help with adding and subtracting decimals?
Can I use the same methods for both addition and subtraction of decimals?
Are there any common mistakes to watch out for when adding or subtracting decimals?
Can decimal addition and subtraction skills be applied in real-life situations?

Adding and Subtracting Decimals exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the learning text Adding and Subtracting Decimals.
  • Calculate the sum of the decimals.

    Hints

    Line up the two decimals with the decimal points and add together.

    For example,

    For this question we add the right hand column up first. $7 + 8 = 15$ We use the $5$ and carry the tens to the next column, moving left.

    Solution

    The correct answer is $12.5$.

    • Line up the two numbers with the decimal point.
    • Add each column from the right to the left.
    • If any column is greater than $9$ write down the units and carry the tens to the next column on the left.
  • Find the sum of the two decimals.

    Hints
    • Line up the numbers with the decimal point
    • If there is a column after the decimal point without a number add in a $0$
    • Start at the right and add up each column

    If the column adds up to a number greater than $9$ we place the units in that column and add the tens to the next column on the left.

    Solution

    The correct answer is $32.42$.

    • Line up the numbers with the decimal point
    • If there is a gap after the decimal point add in a $0$
    • If the column adds up to a number greater than $9$ write the units in the column and add the tens to the next column on the left.
    See steps $1$ to $3$

  • Subtract the decimals.

    Hints
    • Line the decimals up with the decimal points as with addition
    • Subtract the bottom number from the top one
    • If the answer to the column would be a negative we use one of the tens from the next column on the left. For example,

    • Start at the right and move left subtracting each column
    For example,

    Solution
    • We cannot do $3 - 6$ so we add a $10$ from the $7$ and do $13 - 6$
    • The next column now becomes $6 - 3$ which is $3$
    • We next do $6 - 5$ then $1 - 0$ to give us $11.37$
  • Fencing the chicken pen

    Hints

    Line all three numbers up with the decimal points and add together. See the example here.

    Start with the right column and add each column moving left. See the example here.

    • Add $7 + 6 + 8$
    • As this is $21$ we write down the units, $1$ and carry the tens to the column on the left.
    • Now we add $5 + 2 + 6$ and the extra $2$.
    • As this is $15$ we write down the units, $5$ and carry the tens to the column on the left.
    • Nothing to add the $1$ to there so we can write the $1$.

    Solution

    The answer is $22.2$ metres.

    Start with the right column and add each column moving left.

    • Add $3 + 3 + 6$
    • As this is $12$ we write down the units, $2$ and carry the tens to the column on the left.
    • Now we add $8 + 8 + 5$ and the extra $1$.
    • As this is $22$ we write down the units, $2$ and carry the tens to the column on the left.
    • Nothing to add the $2$ to there so we can write the $2$.

  • Find the sum of the decimals.

    Hints

    When adding decimals, line up the numbers with the decimal point. For example,

    Add each column starting at the right and continue left.

    Solution

    The correct answer is $15.76$.

    • Line up the numbers with the decimal point.
    • Add each column starting at the right and continue left.
    See steps $1$ to $4$.

  • Determine the amount of flour by addition and subtraction of decimals.

    Hints

    Jack has used $1.4$ kg and $0.75$ kg of the flour.

    We need to add these together first to find the total flour he has used.

    When we have the total of the flour used, we subtract it from the original amount of $2.4$ kg.

    Solution

    The correct answer is $0.25$ kg of flour left.

    • First, add $1.4 + 0.75 = 2.15$
    • Subtract $2.15$ from $2.4$
    • That is $2.4 - 2.15 = 0.25$
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